Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials

Details Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials

2010-02-04

arxiv.org/abs/1002.1055v1

Mathematics

Dynamical Systems

42 pages, 10 figures

Scientific paper

In this paper, we give a positive answer to the open question: Can there
exist 4 limit cycles in quadratic near-integrable polynomial systems? It is
shown that when a quadratic integrable system has two centers and is perturbed
by quadratic polynomials, it can generate at least 4 limit cycles with (3,1)
distribution. The method of Melnikov function is used.

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